I have had to share my personal cloud with another server behind the same home router. The problem with that is... Can I have two servers behind the same IP and still work with both, each one having it's own apps up and running on the same port numbers?
Well, perhaps there are easier solutions, but the one that worked for me was to create forwarding rules in the router, assigning new ports that redirect the outside traffic to the right port in the internal machine.
Doing so, I only had to change the clients' addresses adding the new external ports to the URL. My goal is to reach my Owncloud service, separated in both machines.
So what you actually want to do is to set up external, non-conflicting ports for your services (80 and 443 in my case, and "upgrade" them to a new range (let's say, 5080 and 5443).
In your router, you configure those ports to redirect traffic to the actual 80 and 443 ports in the internal machine, so you do not have to change any setup in the server.
No need to modify anything on the NoIP configuration either. It just works as fine as usual...
Of course this is a simple solution when you have only four or five clients accessing the server. If you have to reconfigure hundreds of clients, you will probably have to look for a better, more professional option.
Hope this helps to someone with the same problem. Disclaimer: it worked for me, it may not work for you depending on your configuration...